strength vs size, volume vs weight, and total cals (long)

My first question has to do with strength gains. I've seen a lot of people talk about strength gains being neurological, not muscular... in that your body learns how to move more weight, rather than your muscles get stronger and allow you to move more weight. Is that true? Is there any significant muscle change that comes with added strength? Does this depend on how advanced a lifter you are?

Your muscles work too, but it is more neurological than muscular. This is more prevalent with lower reps higher weight (1-3 rep ranges). With the higher weight lower rep strength gains your muscles tend to become more dense, not necessarily larger in size, as they are not filling up with fluid like you get at higher rep ranges. I think at first you will see muscular and neurological gains in weight pushed, the more advanced the more neurological it becomes (From my understanding, correct me if I am wrong here)

So for someone doing bulk/cut cycles, whose goals lie in both their strength-to-weight ratio AND simply looking better...
If strength gains are largely (if not entirely) neurological, and mass gains are largely physical, does it make more sense to do a high volume/low weight routine (by it's nature more geared towards muscle growth) during a bulk than it does during a cut? And conversely, does it make more sense to do a low volume/high weight on a cut?

Depends entirely on your goals, but in theory what you are saying makes sense, but some muscle development does happen at the high weight low reps.
For strength to weight ratio it will always be better to do high weight low reps, in a bulk and cut will be best. If it is to look better/bigger, and be stronger than your idea of heavy low rep on a cut with lighter weight higher rep on a bulk to gain mass, makes sense in theory. (Anyone do this in practice)

My understanding is that you increase the muscle fibers at the low rep high weight, but with the higher reps lower weight you mainly grow the existing muscle fibers by having them tear and rebuild and fill with fluid.

You are no longer a beginner when you can not progress in weight\reps at the rate of a beginner. Not 100%, but generally this will be somewhere close to 1RMS being 1.2xBW Bench, 2xBW Squat, 2.5xBW Deadlift

Eventually you can get into the difference between myofibrilar (comes more from strength training and is smaller visually) and sarcoplasmic (comes more from your mid rep ranges and is caused by fluid storage) hypertrophy.

For some reason it is common for people to think they have to be limited to one rep range. Guess what. You don't! There are good prewritten programs out there that do both such as PHAT and 5/3/1 Boring But Big template. PHAT does 2 upper and 2 lower with one of each being Power (high weight low rep) and one of each being Hypertrophy (mid weight mid rep) I personally plan to move to 5/3/1 BBB template arranged to work muscles 2 times per week. In that one you work each of the big 4 (Squat, Bench, Deadlift, OHP) on a separate day for power, and then do one or two additional lifts in mid weight\rep, I think 4x12.

First and foremost different muscles respond differently to different rep ranges. I've heard (so anecdotal I know, but I tend to trust Paul Carter when it comes to lifting and he's said it) that legs respond better hypertrophy wise to higher rep sets (20+) while your upper body does better with lower rep sets for hypertrophy (8-20). Then again, he's also doing insane crap like curling the bar for 160 reps in a set, or 65 pounds for 100, and his arms are jacked as hell. For 5-3-1 folks, Wendler likes it too and came up with this with him: http://www.t-nation.com/free_online_article/most_recent/100rep_challenge

From my relatively amatuer perspective, it has more to do with how much energy you have than if you're bulking/cutting. High weight, low rep, compound movements tend to give you the most bang for your buck in terms of overall strength and musculature. Make sure you do those, and if you still have the energy afterwards you can add in some bodybuilding stuff to improve/enhance musculature.

I really think the only difference between bulking and cutting workout routines is that you can do more cardio on a bulk and you should either be doing more volume or seeing faster gains with your lifts during that time, too.

I mean you don't have to limit yourself to only one rep range in your lifting routine. To simplify, you could start out with a few 3x5 on compound lifts followed by some 3x8-12 isolations in the same workout. This is harder to do on a full body routine since you will have to use those same muscles again in a couple days, so the additional volume can hinder your next workout. In this case it's best to leave it for your last day of the week assuming you then get 2 days rest afterwards. Once you get to an upper\lower or push\pull or bodypart split, it is easier to manage since you get more rest days before working the same muscle again. People often act like you can only work in one rep range at any given time for some unknown arbitrary reason when there is nothing saying you have to.